Does the Alesis have some sort of 1/4" input jack? I'm pretty sure the TSL has a series FX Loop and would need to go into an "device" and then back to amp. If not, there maybe devices that you could "slave" off ... I think an RC-2 Looper (for instance) has this ability?

I did a crazy thing and ran a Multitrack BR-600 through my FX Loop (DSL50) input was normal Line in and output was (not so normal) heaphone out. It worked...LOL! There was some resulting tone suck, but hey...I had to try!!!